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Transformation Of Functions

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    Draw the graph of y=f(x) where f(x)=x^2

    Describe the transformation which maps y=f(x) to y=f(x-2)

    For this I would basically have to draw the graph x^2 and move the graph 2 places to the right.

    The thing is that I don't understand why are we moving the vertex two places to the right.
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    f(0) = 0

    In the original graph x=0 gives f(0)
    In the second graph x=2 gives f(0)
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    (Original post by TenOfThem)
    f(0) = 0

    In the original graph x=0 gives f(0)
    In the second graph x=2 gives f(0)
    I'm not following.

    Why are you doing x=2 and what are you trying to show by f(x)=0
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    (Original post by zed963)
    I'm not following.

    Why are you doing x=2 and what are you trying to show by f(x)=0
    You asked why the vertex moved 2 places to the right

    The vertex of the original graph is (0,0)

    The vertex of the translated graph is (2,0)
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    Are you trying to say that to make x=0 what do I need to do to make it 0 so in this case add 2
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    (Original post by zed963)
    Are you trying to say that to make x=0 what do I need to do to make it 0 so in this case add 2
    no
    I am saying that to get the vertex in the transformed graph x=2

    f(2-2) = 0
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    (Original post by TenOfThem)
    no
    I am saying that to get the vertex in the transformed graph x=2

    f(2-2) = 0
    Understood.
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    So how do I know which one I should choose for example if I was shown a graph and it told me to state the function and I had two choices to choose from which One would I choose.

    So if I had f(-x) or -f(x)

    What determines which one I choose
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    (Original post by zed963)
    So how do I know which one I should choose for example if I was shown a graph and it told me to state the function and I had two choices to choose from which One would I choose.

    So if I had f(-x) or -f(x)

    What determines which one I choose
    Wether the x has changed [f(-x)] or the y has changed [-f(x)]

    The former transforms parallel to the x-axis whereas the latter transforms parallel to the y-axis

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Updated: August 4, 2012
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